Bottom Line:
Drake's rule is a notoriously universal property of genomes from microbes to mammals-the number of (functional) mutations per-genome per-generation is approximately constant within a phylum, despite the orders of magnitude differences in genome sizes and diverse populations' properties.So far, there is no concise explanation for this phenomenon.A formal model for the storage of genetic information suggests that a genome of any species operates near its maximum informational storage capacity, and the mutation rate per-genome per-generation is near its upper limit, providing a simple explanation for the rule with minimal assumptions.

ABSTRACTHow mutations accumulate in genomes is the central question of molecular evolution theories. However, our understanding of this process is far from complete. Drake's rule is a notoriously universal property of genomes from microbes to mammals-the number of (functional) mutations per-genome per-generation is approximately constant within a phylum, despite the orders of magnitude differences in genome sizes and diverse populations' properties. So far, there is no concise explanation for this phenomenon. A formal model for the storage of genetic information suggests that a genome of any species operates near its maximum informational storage capacity, and the mutation rate per-genome per-generation is near its upper limit, providing a simple explanation for the rule with minimal assumptions.

Fig2: Fluctuation of positional nucleotide frequencies during GI-steady state for different selection weights (W) and population sizes (N). Common fixed parameters are Pm = 2−6, Pti = 2/3, L = 128, nd = 2. In all three subfigures (a, b, c), the line style defines population size: the dash and dot lines correspond to N = 10,000; the solid line to N = 100. a Fluctuations of nucleotide frequencies in a position (P) with selection weights WP = (0.4, 0.38, 0.12, 0.1). b Fluctuations of nucleotide frequencies in a position (P) with selection weights WP = (0.5, 0.3, 0.1, 0.1). c Dynamics of GIsteady

Mentions:
We will call the state of the simulation when the population has already reached equilibrium of the GI-steady state and denotes the mean value of GIρ in equilibrium population as GIsteady. The convergence of GIρ for different parameters is presented in Fig. 1. A biological interpretation for this state that it is a given species maintainable GI value. It can be called a “mutation-selection balance”, however, it is clearly different from Fisher’s balance (Crow 1986), who considered a single site, where in our case the balance is due to the compensatory effects of multiple positive and negative mutations. Other authors considered a balance similar to ours when the frequency of positive mutations is high so that they cannot be easily brought to fixation as in one-by-one case (Sniegowski and Gerrish 2010; Desai and Fisher 2007). This is also different from our approach in a number of aspects—we are not concerned with the fixations at all, and we quantify the limit on genomic complexity—as we discussed earlier, without considerations for this limit, a formal modeling might easily result in “un-physical” solutions. It should be clearly understood that the word “steady” here concerns only the total genetic information (and hence the phenotype), the genomes in the population remain variable, because new mutations still appear with the steady rate (see Fig. 2). The “molecular clock” is ticking, and its empirical steadiness on the evolutionary scale is another indirect hint that the average GI density is a slowly varying parameter. For example, mutations are more frequent in a position with lower GI value, so if density fluctuates strongly on the evolutionary scale, the clock would behave erratically. As we argued (Shadrin et al. 2013), GI increasing (positive) mutations constitute a significant fraction of random mutations (especially when GI in a position is low), thus allowing the same fraction (in the GI equivalent) of negative mutations to remain in the population. The monotonous molecular clock is a simple prediction of the provided model. Alternatively, it can be explained by the neutrality assumption, which seems to be an oversimplification of reality. Also, the provided model shows that the steadiness of the clock is intimately connected with Drake’s rule and the “error threshold”, while the neutral theory is inherently unable to make such connections.Fig. 1

Fig2: Fluctuation of positional nucleotide frequencies during GI-steady state for different selection weights (W) and population sizes (N). Common fixed parameters are Pm = 2−6, Pti = 2/3, L = 128, nd = 2. In all three subfigures (a, b, c), the line style defines population size: the dash and dot lines correspond to N = 10,000; the solid line to N = 100. a Fluctuations of nucleotide frequencies in a position (P) with selection weights WP = (0.4, 0.38, 0.12, 0.1). b Fluctuations of nucleotide frequencies in a position (P) with selection weights WP = (0.5, 0.3, 0.1, 0.1). c Dynamics of GIsteady

Mentions:
We will call the state of the simulation when the population has already reached equilibrium of the GI-steady state and denotes the mean value of GIρ in equilibrium population as GIsteady. The convergence of GIρ for different parameters is presented in Fig. 1. A biological interpretation for this state that it is a given species maintainable GI value. It can be called a “mutation-selection balance”, however, it is clearly different from Fisher’s balance (Crow 1986), who considered a single site, where in our case the balance is due to the compensatory effects of multiple positive and negative mutations. Other authors considered a balance similar to ours when the frequency of positive mutations is high so that they cannot be easily brought to fixation as in one-by-one case (Sniegowski and Gerrish 2010; Desai and Fisher 2007). This is also different from our approach in a number of aspects—we are not concerned with the fixations at all, and we quantify the limit on genomic complexity—as we discussed earlier, without considerations for this limit, a formal modeling might easily result in “un-physical” solutions. It should be clearly understood that the word “steady” here concerns only the total genetic information (and hence the phenotype), the genomes in the population remain variable, because new mutations still appear with the steady rate (see Fig. 2). The “molecular clock” is ticking, and its empirical steadiness on the evolutionary scale is another indirect hint that the average GI density is a slowly varying parameter. For example, mutations are more frequent in a position with lower GI value, so if density fluctuates strongly on the evolutionary scale, the clock would behave erratically. As we argued (Shadrin et al. 2013), GI increasing (positive) mutations constitute a significant fraction of random mutations (especially when GI in a position is low), thus allowing the same fraction (in the GI equivalent) of negative mutations to remain in the population. The monotonous molecular clock is a simple prediction of the provided model. Alternatively, it can be explained by the neutrality assumption, which seems to be an oversimplification of reality. Also, the provided model shows that the steadiness of the clock is intimately connected with Drake’s rule and the “error threshold”, while the neutral theory is inherently unable to make such connections.Fig. 1

Bottom Line:
Drake's rule is a notoriously universal property of genomes from microbes to mammals-the number of (functional) mutations per-genome per-generation is approximately constant within a phylum, despite the orders of magnitude differences in genome sizes and diverse populations' properties.So far, there is no concise explanation for this phenomenon.A formal model for the storage of genetic information suggests that a genome of any species operates near its maximum informational storage capacity, and the mutation rate per-genome per-generation is near its upper limit, providing a simple explanation for the rule with minimal assumptions.

ABSTRACTHow mutations accumulate in genomes is the central question of molecular evolution theories. However, our understanding of this process is far from complete. Drake's rule is a notoriously universal property of genomes from microbes to mammals-the number of (functional) mutations per-genome per-generation is approximately constant within a phylum, despite the orders of magnitude differences in genome sizes and diverse populations' properties. So far, there is no concise explanation for this phenomenon. A formal model for the storage of genetic information suggests that a genome of any species operates near its maximum informational storage capacity, and the mutation rate per-genome per-generation is near its upper limit, providing a simple explanation for the rule with minimal assumptions.